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- Symmetric_group abstract "In abstract algebra, the symmetric group Sn on a finite set of n symbols is the group whose elements are all the permutations of the n symbols, and whose group operation is the composition of such permutations, which are treated as bijective functions from the set of symbols to itself. Since there are n! (n factorial) possible permutations of a set of n symbols, it follows that the order (the number of elements) of the symmetric group Sn is n!.Although symmetric groups can be defined on infinite sets as well, this article discusses only the finite symmetric groups: their applications, their elements, their conjugacy classes, a finite presentation, their subgroups, their automorphism groups, and their representation theory. For the remainder of this article, "symmetric group" will mean a symmetric group on a finite set.The symmetric group is important to diverse areas of mathematics such as Galois theory, invariant theory, the representation theory of Lie groups, and combinatorics. Cayley's theorem states that every group G is isomorphic to a subgroup of the symmetric group on G.".
- Symmetric_group thumbnail Symmetric_group_4;_Cayley_graph_4,9.svg?width=300.
- Symmetric_group wikiPageExternalLink fm28128.pdf.
- Symmetric_group wikiPageExternalLink search?q=Symmetric+Group.
- Symmetric_group wikiPageExternalLink item?id=ASENS_1948_3_65__239_0.
- Symmetric_group wikiPageExternalLink marcus_du_sautoy_symmetry_reality_s_riddle.html.
- Symmetric_group wikiPageID "28901".
- Symmetric_group wikiPageRevisionID "602062055".
- Symmetric_group hasPhotoCollection Symmetric_group.
- Symmetric_group id "p/s091670".
- Symmetric_group title "Symmetric group graph".
- Symmetric_group title "Symmetric group".
- Symmetric_group urlname "SymmetricGroup".
- Symmetric_group urlname "SymmetricGroupGraph".
- Symmetric_group subject Category:Finite_reflection_groups.
- Symmetric_group subject Category:Permutation_groups.
- Symmetric_group subject Category:Symmetry.
- Symmetric_group type Abstraction100002137.
- Symmetric_group type FiniteReflectionGroups.
- Symmetric_group type Group100031264.
- Symmetric_group type PermutationGroups.
- Symmetric_group comment "In abstract algebra, the symmetric group Sn on a finite set of n symbols is the group whose elements are all the permutations of the n symbols, and whose group operation is the composition of such permutations, which are treated as bijective functions from the set of symbols to itself.".
- Symmetric_group label "Groupe symétrique".
- Symmetric_group label "Grupo simétrico".
- Symmetric_group label "Gruppo simmetrico".
- Symmetric_group label "Symmetric group".
- Symmetric_group label "Symmetrische Gruppe".
- Symmetric_group label "Symmetrische groep".
- Symmetric_group label "Симметрическая группа".
- Symmetric_group label "زمرة متماثلة".
- Symmetric_group label "对称群 (n次对称群)".
- Symmetric_group label "対称群".
- Symmetric_group sameAs Symetrická_grupa.
- Symmetric_group sameAs Symmetrische_Gruppe.
- Symmetric_group sameAs Grupo_simétrico.
- Symmetric_group sameAs Groupe_symétrique.
- Symmetric_group sameAs Grup_simetri.
- Symmetric_group sameAs Gruppo_simmetrico.
- Symmetric_group sameAs 対称群.
- Symmetric_group sameAs 대칭군_(군론).
- Symmetric_group sameAs Symmetrische_groep.
- Symmetric_group sameAs m.074_8.
- Symmetric_group sameAs Q849512.
- Symmetric_group sameAs Q849512.
- Symmetric_group sameAs Symmetric_group.
- Symmetric_group wasDerivedFrom Symmetric_group?oldid=602062055.
- Symmetric_group depiction Symmetric_group_4;_Cayley_graph_4,9.svg.
- Symmetric_group isPrimaryTopicOf Symmetric_group.
